Numbers & Operations in Base Ten M03.A-T.1.1.1 Round two- and three-digit whole numbers to the nearest ten or hundred, respectively.
M03.A-T.1.1.2 Add two- and three-digit whole numbers (limit sums from 100 through 1,000) and/or subtract two- and three-digit numbers from three-digit whole numbers.
M03.A-T.1.1.3 Multiply one-digit whole numbers by two-digit multiples of 10 (from 10 through 90).
M03.A-T.1.1.4 Order a set of whole numbers from least to greatest or greatest to least (up through 9,999, and limit sets to no more than four numbers).
M03.A-F.1.1.1 Demonstrate that when a whole or set is partitioned into y equal parts, the fraction 1/y represents 1 part of the whole and/or the fraction x/y represents x equal parts of the whole (limit denominators to 2, 3, 4, 6, and 8; limit numerators to whole numbers less than the denominator; and no simplification necessary).
M03.A-F.1.1.2 Represent fractions on a number line (limit denominators to 2 and 4; limit numerators to whole numbers less than the denominator; and no simplification necessary).
M03.A-F.1.1.3 Recognize and generate simple equivalent fractions (limit the denominators to 1, 2, 3, 4, 6, and 8 and limit numerators to whole numbers less than the denominator). Example 1: 1/2 = 2/4 Example 2: 4/6 = 2/3
M03.A-F.1.1.4 Express whole numbers as fractions, and/or generate fractions that are equivalent to whole numbers (limit denominators to 1, 2, 3, 4, 6, and 8). Example 1: Express 3 in the form 3 = 3/1. Example 2: Recognize that 6/1 = 6.
M03.A-F.1.1.5 Compare two fractions with the same denominator (limit denominators to 1, 2, 3, 4, 6, and 8), using the symbols >, =, or <, and/or justify the conclusions.
Fractions on a number line with a denominator of 3, 6, and 8
Operations & Algebraic Thinking M03.B-O.1.1.1 Interpret and/or describe products of whole numbers (up to and including 10 × 10). Example 1: Interpret 35 as the total number of objects in 5 groups, each containing 7 objects. Example 2: Describe a context in which a total number of objects can be expressed as 5 × 7
M03.B-O.1.1.2 Interpret and/or describe whole-number quotients of whole numbers (limit dividends through 50 and limit divisors and quotients through 10). Example 1: Interpret 48 ÷ 8 as the number of objects in each share when 48 objects are partitioned equally into 8 shares, or as a number of shares when 48 objects are partitioned into equal shares of 8 objects each. Example 2: Describe a context in which a number of shares or a number of groups can be expressed as 48 ÷ 8.
M03.B-O.1.2.1 Use multiplication (up to and including 10 × 10) and/or division (limit dividends through 50 and limit divisors and quotients through 10) to solve word problems in situations involving equal groups, arrays, and/or measurement quantities.
M03.B-O.1.2.2 Determine the unknown whole number in a multiplication (up to and including 10 × 10) or division (limit dividends through 50 and limit divisors and quotients through 10) equation relating three whole numbers. Example: Determine the unknown number that makes an equation true.
M03.B-O.2.1.1 Apply the commutative property of multiplication (not identification or definition of the property).
M03.B-O.2.1.2 Apply the associative property of multiplication (not identification or definition of the property).
M03.B-O.2.2.1 Interpret and/or model division as a multiplication equation with an unknown factor. Example: Find 32 ÷ 8 by solving 8 × ? = 32.
M03.B-O.3.1.1 Solve two-step word problems using the four operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers.
M03.B-O.3.1.2 Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers.
M03.B-O.3.1.3 Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers.
M03.B-O.3.1.4 Solve two-step equations using order of operations (equation is explicitly stated with no grouping symbols).
M03.B-O.3.1.7 Identify the missing symbol (+ , –, ×, ÷, <, >, and =) that makes a number sentence true
Students don’t use a symbol for an unknown value.
M03.B-O.3.1.5 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or explain them using properties of operations. Example 1: Observe that 4 times a number is always even. Example 2: Explain why 6 times a number can be decomposed into three equal addends.
M03.B-O.3.1.6 Create or match a story to a given combination of symbols (+, –, ×, ÷, <, >, and =) and numbers. .
Geometry M03.C-G.1.1.1 Explain that shapes in different categories may share attributes and that the shared attributes can define a larger category. Example 1: A rhombus and a rectangle are both quadrilaterals since they both have exactly four sides. Example 2: A triangle and a pentagon are both polygons since they are both multi-sided plane figures.
M03.C-G.1.1.2 Recognize rhombi, rectangles, and squares as examples of quadrilaterals and/or draw examples of quadrilaterals that do not belong to any of these subcategories.
M03.C-G.1.1.3 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Example 1: Partition a shape into 4 parts with equal areas. Example 2: Describe the area of each of 8 equal parts as 1/8 of the area of the shape.
Measurement & Data M03.D-M.1.1.1 Tell, show, and/or write time (analog) to the nearest minute.
M03.D-M.1.1.2 Calculate elapsed time to the minute in a given situation (total elapsed time limited to 60 minutes or less).
M03.D-M.1.2.1 Measure and estimate liquid volumes and masses of objects using standard units (cups [c], pints [pt], quarts [qt], gallons [gal ], ounces [oz.], and pounds [lb]) and metric units (liters [l], grams [g], and kilograms [kg]).
M03.D-M.1.2.2 Add, subtract, multiply, and divide to solve one- step word problems involving masses or liquid volumes that are given in the same units.
M03.D-M.1.2.3 Use a ruler to measure lengths to the nearest quarter inch or centimeter
M03.D-M.1.3.1 Compare total values of combinations of coins (penny, nickel, dime, and quarter) and/or dollar bills less than $5.00.
M03.D-M.1.3.2 Make change for an amount up to $5.00 with no more than $2.00 change given (penny, nickel, dime, quarter, and dollar).
M03.D-M.1.3.3 Round amounts of money to the nearest dollar M03.D-M.2.1.1 Complete a scaled pictograph and a scaled bar graph to represent a data set with several categories (scales limited to 1, 2, 5, and 10).
M03.D-M.2.1.2 Solve one- and two-step problems using information to interpret data presented in scaled pictographs and scaled bar graphs (scales limited to 1, 2, 5, and 10). Example 1: (One-step) “Which category is the largest?” Example 2: (Two-step) “How many more are in category A than in category B?”
M03.D-M.2.1.3 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Display the data by making a line plot, where the horizontal scale is marked in appropriate units—whole numbers, halves, or quarters.
M03.D-M.2.1.4 Translate information from one type of display to another. Limit to pictographs, tally charts, bar graphs, and tables. Example: Convert a tally chart to a bar graph.
M03.D-M.3.1.1 Measure areas by counting unit squares (square cm, square m, square in., square ft, and non-standard square units).
M03.D-M.3.1.2 Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
M03.D-M.4.1.1 Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, exhibiting rectangles with the same perimeter and different areas, and exhibiting rectangles with the same area and different perimeters. Use the same units throughout the problem.
Grade 4
Numbers and Operations in Base Ten M04.A-T.1.1.1 Demonstrate an understanding that in a multi-digit whole number (through 1,000,000), a digit in one place represents ten times what it represents in the place to its right. Example: Recognize that in the number 770, the 7 in the hundreds place is ten times the 7 in the tens place.
M04.A-T.1.1.2 Read and write whole numbers in expanded, standard, and word form through 1,000,000.
M04.A-T.1.1.3 Compare two multi-digit numbers through 1,000,000 based on meanings of the digits in each place, using >, =, and < symbols.
M04.A-T.1.1.4 Round multi-digit whole numbers (through 1,000,000) to any place.
M04.A-T.2.1.1 Add and subtract multi-digit whole numbers (limit sums and subtrahends up to and including 1,000,000).
M04.A-T.2.1.2 Multiply a whole number of up to four digits by a one-digit whole number and multiply 2 two-digit numbers.
M04.A-T.2.1.3 Divide up to four-digit dividends by one-digit divisors with answers written as whole-number quotients and remainders.
M04.A-T.2.1.4 Estimate the answer to addition, subtraction, and multiplication problems using whole numbers through six digits (for multiplication, no more than 2 digits × 1 digit, excluding powers of 10)
M04.A-F.1.1.1 Recognize and generate equivalent fractions.
M04.A-F.1.1.2 Compare two fractions with different numerators and different denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the symbols >, =, or < and justify the conclusions.
M04.A-F.1.1.2 Compare two fractions with different numerators and different denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the symbols >, =, or < and justify the conclusions M04.A-F.2.1.1 Add and subtract fractions with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; answers do not need to be simplified; and no improper fractions as the final answer).
M04.A-F.2.1.2 Decompose a fraction or a mixed number into a sum of fractions with the same denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100), recording the decomposition by an equation. Justify decompositions (e.g., by using a visual fraction model). Example 1: 3/8 = 1/8 + 1/8 + 1/ 8 OR 3/8 = 1/8 + 2/8 Example 2: 2 1/12 = 1 + 1 + 1/12 = 12/12 + 12/12 + 1/12
M04.A-F.2.1.3 Add and subtract mixed numbers with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; no regrouping with subtraction; fractions do not need to be simplified; and no improper fractions as the final answers).
M04.A-F.2.1.4 Solve word problems involving addition and subtraction of fractions referring to the same whole or set and having like denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).
M04.A-F.3.1.2 Use decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100 and vice versa.
M04.A-F.3.1.3 Compare two decimals to hundredths using the symbols >, =, or <, and justify the conclusions.
M04.A-F.2.1.5 Multiply a whole number by a unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 5 × (1/4) = 5/4
M04.A-F.2.1.6 Multiply a whole number by a non-unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 3 × (5/6) = 15/6
M04.A-F.2.1.7 Solve word problems involving multiplication of a whole number by a fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).
M04.A-F.3.1.1 Add two fractions with respective denominators 10 and 100. Example: Express 3/10 as 30/100, and add 3/10 + 4/100 = 30/100 + 4/100 = 34/100.
Operations & Algebraic Thinking M04.B-O.1.1.1 Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. Example 1: Interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Example 2: Know that the statement 24 is 3 times as many as 8 can be represented by the equation 24 = 3 × 8 or 24 = 8 × 3.
M04.B-O.1.1.2 Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Example: Know that 3 × 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects not just 3 more objects.
M04.B-O.1.1.3 Solve multi-step word problems posed with whole numbers using the four op erations. Answers will be either whole numbers or have remainders that must be interpreted yielding a final answer that is a whole number. Represent these problems using equations with a symbol or letter standing for the unknown quantity.
M04.B-O.1.1.4 Identify the missing symbol (+ , –, ×, ÷, =, <, and >) that makes a number sentence true (single-digit divisor only).
M04.B-O.2.1.1 Find all factor pairs for a whole number in the interval 1 through 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the interval 1 through 100 is a multiple of a given one- digit number. Determine whether a given whole number in the interval 1 through 100 is prime or composite. M04.B-O.3.1.1 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Example 1: Given the rule “add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms alternate between odd and even numbers. Example 2: Given the rule “increase the number of sides by 1” and starting with a triangle, observe that the tops of the shapes alternate between a side and a vertex.
M04.B-O.3.1.2 Determine the missing elements in a function table (limit to +, –, or × and to whole numbers or money).
M04.B-O.3.1.3 Determine the rule for a function given a table (limit to +, –, or × and to whole numbers).
Geometry M04.C-G.1.1.1 Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in two- dimensional figures.
M04.C-G.1.1.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
M04.C-G.1.1.3 Recognize a line of symmetry for a two- dimensional figure as a line across the figure such that the figure can be folded along the line into mirroring parts. Identify line-symmetric figures and draw lines of symmetry (up to two lines of symmetry).
Measurement & Data M04.D-M.1.1.1 Know relative sizes of measurement units within one system of units including standard units (in., ft, yd, mi; oz., lb; and c, pt, qt, gal), metric units (cm, m, km; g, kg; and mL, L), and time (sec, min, hr, day, wk, mo, and yr). Within a single system of measurement, express measurements in a larger unit in terms ofa smaller unit. A table of equivalencies will be provided. Example 1: Know that 1 kg is 1,000 times as heavy as 1 g. Example 2: Express the length of a 4-foot snake as 48 in. M04.D-M.1.1.2 Use the four operations to solve word problems involving distances, intervals of time (such as elapsed time), liquid volumes, masses of objects; money, including problems involving simple fractions or decimals; and problems that require expressing measurements given in a larger unit in terms of a smaller unit.
M04.D-M.1.1.3 Apply the area and perimeter formulas for rectangles in real-world and mathematical problems (may include finding a missing side length). Whole numbers only. The formulas will be provided.
M04.D-M.1.1.4 Identify time (analog or digital) as the amount of minutes before or after the hour. Example 1: 2:50 is the same as 10 minutes before 3:00. Example 2: Quarter past six is the same as 6:15.
M04.D-M.2.1.3 Translate information from one type of display to another (table, chart, bar graph, or pictograph).
M04.D-M.3.1.1 Measure angles in whole-number degrees using a protractor. With the aid of a protractor, sketch angles of specified measure. M04.D-M.3.1.2 Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. (Angles must be adjacent and non-overlapping.)
M04.D-M.2.1.1 Make a line plot to display a data set of measurements in fractions of a unit (e.g., intervals of 1/2, 1/4, or 1/8).
M04.D-M.2.1.2 Solve problems involving addition and subtraction of fractions by using information presented in line plots (line plots must be labeled with common denominators, such as 1/4, 2/4, 3/4).
Grade 5
Numbers & Operations in Base Ten M05.A-T.1.1.1 Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Example: Recognize that in the number 770, the 7 in the tens place is 1/10 the 7 in the hundreds place.
M05.A-T.1.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10. Example 1: 4 × 102 = 400 Example 2: 0.05 ÷ 103 = 0.00005
M05.A-T.1.1.4 Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols.
M05.A-T.1.1.5 Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place).
M05.A-T.2.1.1 Multiply multi-digit whole numbers (not to exceed three-digit by three-digit).
M05.A-T.2.1.2 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.
M05.A-T.2.1.3 Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals).
Numbers & Operations – Fractions M05.A-F.1.1.1 Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Example: 2/3 + 5/4 = 8/12 + 15/12 = 23/12
M05.A-F.2.1.1 Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers).
M05.A-F.2.1.2 Multiply a fraction (including mixed numbers) by a fraction.
M05.A-F.2.1.3 Demonstrate an understanding of multiplication as scaling (resizing). Example 1: Comparing the size of a product to the size of one factor on the basis of the size of the other factor without performing the indicated multiplication. Example 2: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than1 results in a product smaller than the given number.
M05.A-F.2.1.4 Divide unit fractions by whole numbers and whole numbers by unit fractions.
Operations & Algebraic Thinking M05.B-O.1.1.1 Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols.
M05.B-O.1.1.2 Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Example 1: Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Example 2: Recognize that 3 × (18,932 + 921) is three times as large as 18,932 + 921 without having to calculate the indicated sum or product.
Not brackets or braces M05.B-O.2.1.1 Generate two numerical patterns using two given rules. Example: Given the rule “add 3” and the starting number 0 and given the rule “add 6” and the starting number 0, generate terms in the resulting sequences.
M05.B-O.2.1.2 Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Example: Given two patterns in which the first pattern follows the rule “add 8” and the second pattern follows the rule “add 2,” observe that the terms in the first pattern are 4 times the size of the terms in the second pattern.
Geometry M05.C-G.1.1.1 Identify parts of the coordinate plane ( x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I.
M05.C-G.2.1.1 Classify two-dimensional figures in a hierarchy based on properties. Example 1: All polygons have at least three sides, and pentagons are polygons, so all pentagons have at least three sides. Example 2: A rectangle is a parallelogram, which is a quadrilateral, which is a polygon; so, a rectangle can be classified as a parallelogram, as a quadrilateral, and as a polygon
M05.C-G.1.1.2 Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation.
Measurement & Data M05.D-M.1.1.1 Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Example: Convert 5 cm to meters.
M05.D-M.2.1.2 Display and interpret data shown in tallies, tables, charts, pictographs, bar graphs, and line graphs, and use a title, appropriate scale, and labels. A grid will be provided to display data on bar graphs or line graphs.
M05.D-M.3.1.1 Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems. Formulas will be provided.
M05.D-M.3.1.2 Find volumes of solid figures composed of two non-overlapping right rectangular prisms.
M05.D-M.2.1.1 Solve problems involving computation of fractions by using information presented in line plots.
Grade 3
M03.A-T.1.1.1
Round two- and three-digit whole numbers to the nearest ten or hundred, respectively.
M03.A-T.1.1.2
Add two- and three-digit whole numbers (limit
sums from 100 through 1,000) and/or subtract
two- and three-digit numbers from three-digit
whole numbers.
M03.A-T.1.1.3
Multiply one-digit whole numbers by two-digit
multiples of 10 (from 10 through 90).
M03.A-T.1.1.4
Order a set of whole numbers from least to
greatest or greatest to least (up through 9,999, and limit sets to no more than four numbers).
M03.A-F.1.1.1
Demonstrate that when a whole or set is
partitioned into y equal parts, the fraction 1/y
represents 1 part of the whole and/or the fraction x/y represents x
equal parts of the whole (limit
denominators to 2, 3, 4,
6, and 8; limit numerators
to whole numbers less than the denominator; and no simplification necessary).
M03.A-F.1.1.2
Represent fractions on a number line (limit
denominators to 2 and 4; limit numerators
to whole numbers less than the denominator; and no simplification necessary).
M03.A-F.1.1.3
Recognize and generate simple equivalent
fractions (limit the denominators to 1, 2, 3, 4, 6,
and 8 and limit numerators to whole numbers less
than the denominator).
Example 1:
1/2 = 2/4
Example 2:
4/6 = 2/3
M03.A-F.1.1.4
Express whole numbers as fractions, and/or
generate fractions that are equivalent to whole
numbers (limit denominators to 1, 2, 3, 4, 6, and
8).
Example 1:
Express 3 in the form 3 = 3/1.
Example 2:
Recognize that 6/1 = 6.
M03.A-F.1.1.5
Compare two fractions with the same denominator (limit denominators to 1, 2, 3, 4, 6, and 8), using the symbols >, =, or <, and/or justify the conclusions.
M03.B-O.1.1.1
Interpret and/or describe products of whole
numbers (up to and including 10 × 10).
Example 1: Interpret 35 as the total number of
objects in 5 groups, each containing 7 objects.
Example 2: Describe a context in which a total
number of objects can be expressed as 5 × 7
M03.B-O.1.1.2
Interpret and/or describe whole-number quotients of whole numbers (limit dividends through 50 and limit divisors and quotients through 10).
Example 1:
Interpret 48 ÷ 8 as the number of
objects in each share when 48 objects are
partitioned equally into 8 shares, or as a number of
shares when 48 objects are partitioned into equal
shares of 8 objects each.
Example 2:
Describe a context in which a number
of shares or a number of groups can be expressed as 48 ÷ 8.
M03.B-O.1.2.1
Use multiplication (up to and including 10 × 10)
and/or division (limit dividends through 50 and limit divisors and quotients through 10) to solve word problems in situations involving equal groups, arrays, and/or measurement quantities.
M03.B-O.1.2.2
Determine the unknown whole number in a
multiplication (up to and including 10 × 10) or
division (limit dividends through 50 and limit
divisors and quotients through 10) equation
relating three whole numbers.
Example:
Determine the unknown number that
makes an equation true.
M03.B-O.2.1.1
Apply the commutative property of multiplication
(not identification or definition of the property).
M03.B-O.2.1.2
Apply the associative property of multiplication (not identification or definition of the property).
M03.B-O.2.2.1
Interpret and/or model division as a multiplication
equation with an unknown factor.
Example:
Find 32 ÷ 8 by solving 8 × ? = 32.
M03.B-O.3.1.1
Solve two-step word problems using the four
operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers.
M03.B-O.3.1.2
Represent two-step word problems using
equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers.
M03.B-O.3.1.3
Assess the reasonableness of answers. Limit
problems posed with whole numbers and having whole-number answers.
M03.B-O.3.1.4
Solve two-step equations using order of operations
(equation is explicitly stated with no grouping
symbols).
M03.B-O.3.1.7
Identify the missing symbol (+
, –, ×, ÷, <, >, and =)
that makes a number sentence true
M03.B-O.3.1.5
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or
explain them using properties of operations.
Example 1:
Observe that 4 times a number is
always even.
Example 2:
Explain why 6 times a number can be
decomposed into three equal addends.
M03.B-O.3.1.6
Create or match a story to a given combination of
symbols (+, –, ×, ÷, <,
>, and =) and numbers.
.
M03.C-G.1.1.1
Explain that shapes in different categories may
share attributes and that the shared attributes can
define a larger category.
Example 1:
A rhombus and a rectangle are both
quadrilaterals since they both have exactly four
sides.
Example 2:
A triangle and a pentagon are both
polygons since they are both multi-sided plane
figures.
M03.C-G.1.1.2
Recognize rhombi, rectangles, and squares as
examples of quadrilaterals and/or draw examples
of quadrilaterals that do not belong to any of these
subcategories.
M03.C-G.1.1.3
Partition shapes into parts with equal areas.
Express the area of each part as a unit fraction of
the whole.
Example 1:
Partition a shape into 4 parts with
equal areas.
Example 2:
Describe the area of each of 8 equal
parts as 1/8 of the area of the shape.
M03.D-M.1.1.1
Tell, show, and/or write time (analog) to the
nearest minute.
M03.D-M.1.1.2
Calculate elapsed time to the minute in a given
situation (total elapsed time limited to 60 minutes
or less).
M03.D-M.1.2.1
Measure and estimate liquid volumes and masses
of objects using standard units (cups [c], pints [pt],
quarts [qt], gallons [gal
], ounces [oz.], and
pounds [lb]) and metric units (liters [l], grams [g],
and kilograms [kg]).
M03.D-M.1.2.2
Add, subtract, multiply, and divide to solve one-
step word problems involving masses or liquid
volumes that are given in the same units.
M03.D-M.1.2.3
Use a ruler to measure lengths to the nearest
quarter inch or centimeter
M03.D-M.1.3.1
Compare total values of combinations of coins
(penny, nickel, dime, and quarter) and/or dollar
bills less than $5.00.
M03.D-M.1.3.2
Make change for an amount up to $5.00 with no
more than $2.00 change given (penny, nickel,
dime, quarter, and dollar).
M03.D-M.1.3.3
Round amounts of money to the nearest dollar
M03.D-M.2.1.1
Complete a scaled pictograph and a scaled bar
graph to represent a data set with several
categories (scales limited to 1, 2, 5, and 10).
M03.D-M.2.1.2
Solve one- and two-step problems using
information to interpret data presented in scaled
pictographs and scaled bar graphs (scales limited
to 1, 2, 5, and 10).
Example 1:
(One-step) “Which category is the
largest?”
Example 2:
(Two-step) “How many more are in
category A than in category B?”
M03.D-M.2.1.3
Generate measurement data by measuring lengths
using rulers marked with halves and fourths of an
inch. Display the data by making a line plot, where
the horizontal scale is marked in appropriate
units—whole numbers, halves, or quarters.
M03.D-M.2.1.4
Translate information from one type of display to
another. Limit to pictographs, tally charts, bar
graphs, and tables.
Example:
Convert a tally chart to a bar graph.
M03.D-M.3.1.1
Measure areas by counting unit squares
(square cm, square m, square in., square ft, and
non-standard square units).
M03.D-M.3.1.2
Multiply side lengths to find areas of rectangles with
whole-number side lengths in the context of solving
real-world and mathematical problems, and
represent whole-number products as rectangular
areas in mathematical reasoning.
M03.D-M.4.1.1
Solve real-world and mathematical problems
involving perimeters of polygons, including finding
the perimeter given the side lengths, finding an
unknown side length, exhibiting rectangles with the
same perimeter and different areas, and exhibiting
rectangles with the same area and different
perimeters. Use the same units throughout the
problem.
Grade 4
M04.A-T.1.1.1
Demonstrate an understanding that in a multi-digit
whole number (through 1,000,000), a digit in one
place represents ten times what it represents in
the place to its right.
Example:
Recognize that in the number 770, the 7
in the hundreds place is ten times the 7 in the tens
place.
M04.A-T.1.1.2
Read and write whole numbers in expanded,
standard, and word form through 1,000,000.
M04.A-T.1.1.3
Compare two multi-digit numbers through
1,000,000 based on meanings of the digits in each
place, using >, =, and < symbols.
M04.A-T.1.1.4
Round multi-digit whole numbers (through
1,000,000) to any place.
M04.A-T.2.1.1
Add and subtract multi-digit whole numbers (limit
sums and subtrahends up to and including
1,000,000).
M04.A-T.2.1.2
Multiply a whole number of up to four digits by a
one-digit whole number and multiply 2 two-digit
numbers.
M04.A-T.2.1.3
Divide up to four-digit dividends by one-digit
divisors with answers written as whole-number
quotients and remainders.
M04.A-T.2.1.4
Estimate the answer to addition, subtraction, and
multiplication problems using whole numbers
through six digits (for multiplication, no more than
2 digits × 1 digit, excluding powers of 10)
M04.A-F.1.1.1
Recognize and generate equivalent fractions.
M04.A-F.1.1.2
Compare two fractions with different numerators
and different denominators (denominators limited
to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the
symbols >, =, or < and justify the conclusions.
M04.A-F.1.1.1
Recognize and generate equivalent fractions.
M04.A-F.1.1.2
Compare two fractions with different numerators
and different denominators (denominators limited
to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the
symbols >, =, or < and justify the conclusions
M04.A-F.2.1.1
Add and subtract fractions with a common
denominator (denominators limited to 2, 3, 4, 5, 6,
8, 10, 12, and 100; answers do not need to be
simplified; and no improper fractions as the
final answer).
M04.A-F.2.1.2
Decompose a fraction or a mixed number into a
sum of fractions with the same denominator
(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and
100), recording the decomposition by an equation.
Justify decompositions (e.g., by using a visual
fraction model).
Example 1:
3/8 = 1/8 + 1/8 + 1/
8 OR 3/8 = 1/8 + 2/8
Example 2:
2 1/12 = 1 + 1 + 1/12 =
12/12 + 12/12 + 1/12
M04.A-F.2.1.3
Add and subtract mixed numbers with a common
denominator (denominators limited to 2, 3, 4, 5, 6,
8, 10, 12, and 100; no regrouping with subtraction;
fractions do not need to be simplified; and no
improper fractions as the final answers).
M04.A-F.2.1.4
Solve word problems involving addition and
subtraction of fractions referring to the same whole
or set and having like denominators (denominators
limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).
M04.A-F.3.1.2
Use decimal notation for fractions with
denominators 10 or 100.
Example:
Rewrite 0.62 as 62/100 and vice versa.
M04.A-F.3.1.3
Compare two decimals to hundredths using the
symbols >, =, or <, and justify the conclusions.
Multiply a whole number by a unit fraction
(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and
100 and final answers do not need to be
simplified or written as a mixed number).
Example:
5 × (1/4) = 5/4
M04.A-F.2.1.6
Multiply a whole number by a non-unit fraction
(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and
100 and final answers do not need to be
simplified or written as a mixed number).
Example:
3 × (5/6) = 15/6
M04.A-F.2.1.7
Solve word problems involving multiplication of a
whole number by a fraction (denominators limited
to 2, 3, 4, 5, 6, 8, 10, 12, and 100).
M04.A-F.3.1.1
Add two fractions with respective denominators 10
and 100.
Example:
Express 3/10 as 30/100, and add
3/10 + 4/100 = 30/100 + 4/100 = 34/100.
M04.B-O.1.1.1
Interpret a multiplication equation as a comparison.
Represent verbal statements of multiplicative
comparisons as multiplication equations.
Example 1:
Interpret 35 = 5 × 7 as a statement that
35 is 5 times as many as 7 and 7 times as many
as 5.
Example 2:
Know that the statement 24 is 3 times
as many as 8 can be represented by the equation
24 = 3 × 8 or 24 = 8 × 3.
M04.B-O.1.1.2
Multiply or divide to solve word problems involving
multiplicative comparison, distinguishing
multiplicative comparison from additive
comparison.
Example:
Know that 3 × 4 can be used to
represent that Student A has 4 objects and
Student B has 3 times as many
objects not just
3 more objects.
M04.B-O.1.1.3
Solve multi-step word problems posed with whole
numbers using the four op
erations. Answers will be
either whole numbers or have remainders that
must be interpreted yielding a final answer that is a
whole number. Represent these problems using
equations with a symbol or letter standing for the
unknown quantity.
M04.B-O.1.1.4
Identify the missing symbol (+
, –, ×, ÷, =, <, and >)
that makes a number sentence true (single-digit
divisor only).
M04.B-O.2.1.1
Find all factor pairs for a whole number in the
interval 1 through 100. Recognize that a whole
number is a multiple of each of its factors.
Determine whether a given whole number in the
interval 1 through 100 is a multiple of a given one-
digit number. Determine whether a given whole
number in the interval 1 through 100 is prime or
composite.
M04.B-O.3.1.1
Generate a number or shape pattern that follows a
given rule. Identify apparent features of the pattern
that were not explicit in the rule itself.
Example 1:
Given the rule “add 3” and the starting
number 1, generate terms in the resulting
sequence and observe that the terms alternate
between odd and even numbers.
Example 2:
Given the rule “increase the number of
sides by 1” and starting with a triangle, observe
that the tops of the shapes alternate between a
side and a vertex.
M04.B-O.3.1.2
Determine the missing elements in a function table
(limit to +, –, or × and to whole numbers or
money).
M04.B-O.3.1.3
Determine the rule for a function given a table
(limit to +, –, or ×
and to whole numbers).
M04.C-G.1.1.1
Draw points, lines, line segments, rays, angles
(right, acute, and obtuse), and perpendicular
and parallel lines. Identify these in two-
dimensional figures.
M04.C-G.1.1.2
Classify two-dimensional figures based on the
presence or absence of parallel or perpendicular
lines or the presence or absence of angles of a
specified size. Recognize right triangles as a
category, and identify right triangles.
M04.C-G.1.1.3
Recognize a line of symmetry for a two-
dimensional figure as a line across the figure such
that the figure can be folded along the line into
mirroring parts. Identify line-symmetric figures and
draw lines of symmetry
(up to two lines of
symmetry).
M04.D-M.1.1.1
Know relative sizes of measurement units within
one system of units including standard units (in.,
ft, yd, mi; oz., lb; and c, pt, qt, gal), metric units
(cm, m, km; g, kg; and mL, L), and time (sec, min,
hr, day, wk, mo, and yr). Within a single system of
measurement, express measurements in a larger
unit in terms ofa smaller unit.
A table of
equivalencies will be provided.
Example 1:
Know that 1 kg is 1,000 times as
heavy as 1 g.
Example 2:
Express the length of a 4-foot snake
as 48 in.
M04.D-M.1.1.2
Use the four operations to solve word problems
involving distances, intervals of time (such as
elapsed time), liquid volumes, masses of objects;
money, including problems involving simple
fractions or decimals; and problems that require
expressing measurements given in a larger unit in
terms of a smaller unit.
M04.D-M.1.1.3
Apply the area and perimeter formulas for
rectangles in real-world and mathematical
problems (may include finding a missing side
length). Whole numbers only.
The formulas will
be provided.
M04.D-M.1.1.4
Identify time (analog or digital) as the amount of
minutes before or after the hour.
Example 1:
2:50 is the same as 10 minutes before
3:00.
Example 2:
Quarter past six is the same as 6:15.
M04.D-M.2.1.3
Translate information from one type of display to
another (table, chart, bar graph, or pictograph).
M04.D-M.3.1.1
Measure angles in whole-number degrees using a
protractor. With the aid of a protractor, sketch
angles of specified measure.
M04.D-M.3.1.2
Solve addition and subtraction problems to find
unknown angles on a diagram in real-world and
mathematical problems. (Angles must be adjacent
and non-overlapping.)
Make a line plot to display a data set of
measurements in fractions of a unit (e.g., intervals
of 1/2, 1/4, or 1/8).
M04.D-M.2.1.2
Solve problems involving addition and subtraction
of fractions by using information presented in line
plots (line plots must be labeled with common
denominators, such as 1/4, 2/4, 3/4).
Grade 5
M05.A-T.1.1.1
Demonstrate an understanding that in a multi-digit
number, a digit in one place represents 1/10 of
what it represents in the place to its left.
Example:
Recognize that in the number 770, the
7 in the tens place is 1/10 the 7 in the hundreds
place.
M05.A-T.1.1.2
Explain patterns in the number of zeros of the
product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.
Example 1:
4 × 102 = 400
Example 2:
0.05 ÷ 103 = 0.00005
M05.A-T.1.1.3
Read and write decimals to thousandths using
base-ten numerals, word form, and expanded
form.
Example:
347.392 = 300 + 40 + 7 + 0.3 + 0.09 +
0.002 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (0.1) +
9 × (0.01) + 2 × (0.001)
M05.A-T.1.1.4
Compare two decimals to thousandths based on
meanings of the digits in each place using >, =,
and < symbols.
M05.A-T.1.1.5
Round decimals to any place (limit rounding to
ones, tenths, hundredths, or thousandths place).
M05.A-T.2.1.1
Multiply multi-digit whole numbers (not to exceed three-digit by three-digit).
M05.A-T.2.1.2
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.
M05.A-T.2.1.3
Add, subtract, multiply, and divide decimals to
hundredths (no divisors with decimals).
M05.A-F.1.1.1
Add and subtract fractions (including mixed
numbers) with unlike denominators. (May include
multiple methods and representations.)
Example:
2/3 + 5/4 = 8/12 + 15/12 = 23/12
M05.A-F.2.1.1
Solve word problems involving division of whole
numbers leading to answers in the form of fractions
(including mixed numbers).
M05.A-F.2.1.2
Multiply a fraction (including mixed numbers) by a fraction.
M05.A-F.2.1.3
Demonstrate an understanding of multiplication as
scaling (resizing).
Example 1:
Comparing the size of a product to the
size of one factor on the basis of the size of the other factor without performing the indicated multiplication.
Example 2:
Explaining why multiplying a given
number by a fraction greater than 1 results in a
product greater than the given number
(recognizing multiplication by whole numbers
greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than1 results in a product smaller than the given number.
M05.A-F.2.1.4
Divide unit fractions by whole numbers and whole numbers by unit fractions.
M05.B-O.1.1.1
Use multiple grouping symbols (parentheses,
brackets, or braces) in numerical expressions and evaluate expressions containing these symbols.
M05.B-O.1.1.2
Write simple expressions that model calculations
with numbers and interpret numerical expressions
without evaluating them.
Example 1:
Express the calculation “add 8 and 7,
then multiply by 2” as 2 × (8 + 7).
Example 2:
Recognize that 3 × (18,932 + 921) is
three times as large as 18,932 + 921 without
having to calculate the indicated sum or product.
M05.B-O.2.1.1
Generate two numerical patterns using two given rules.
Example:
Given the rule “add 3” and the starting
number 0 and given the rule “add 6” and the
starting number 0, generate terms in the resulting sequences.
M05.B-O.2.1.2
Identify apparent relationships between
corresponding terms of two patterns with the same starting numbers that follow different rules.
Example:
Given two patterns in which the first
pattern follows the rule “add 8” and the second
pattern follows the rule “add 2,” observe that the
terms in the first pattern are 4 times the size of the
terms in the second pattern.
M05.C-G.1.1.1
Identify parts of the coordinate plane (
x-axis, y-axis,
and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to
quadrant I.
M05.C-G.2.1.1
Classify two-dimensional figures in a hierarchy
based on properties.
Example 1:
All polygons have at least three sides,
and pentagons are polygons, so all pentagons
have at least three sides.
Example 2:
A rectangle is a parallelogram, which is
a quadrilateral, which is a polygon; so, a rectangle
can be classified as a parallelogram, as a
quadrilateral, and as a polygon
Represent real-world and mathematical problems
by plotting points in quadrant I of the coordinate
plane and interpret coordinate values of points in
the context of the situation.
M05.D-M.1.1.1
Convert between different-sized measurement
units within a given measurement system.
A table
of equivalencies will be provided.
Example:
Convert 5 cm to meters.
M05.D-M.2.1.2
Display and interpret data shown in tallies, tables,
charts, pictographs, bar graphs, and line graphs,
and use a title, appropriate scale, and labels. A
grid will be provided to display data on bar graphs
or line graphs.
M05.D-M.3.1.1
Apply the formulas
V = l × w × h and V = B × h for
rectangular prisms to find volumes of right
rectangular prisms with whole-number edge
lengths in the context of solving real-world and
mathematical problems.
Formulas will be
provided.
M05.D-M.3.1.2
Find volumes of solid figures composed of two
non-overlapping right rectangular prisms.
Solve problems involving computation of fractions
by using information presented in line plots.